You need to have cards that use spell counters and you probably know that you can use small items like pennies to mark them. (make sure no one steals them)
I suggest following the link provide, as it will show you all the cards that use or produce spell counters.
Cards like Royal Magical Library are good for Spell Counters as one is generated every time a spell card resolves.
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The spell counters will be lost, they will not be transferred to the new monster.
'Shield and Sword', a Normal Spell Card, can do that.
No, it doesn't end the battle phase.
No, there isn't. Unless you count a Field Spell Card, which is a spell card but has its own zone, so technically you can have 6 spells active.
There is no real hard limit - as long as you've got a spell card in hand, and a slot in the S/T zone for it to go, then you can activate it.